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Calculus and Optimization for Machine Learning
Week 4
Practice Quiz #2

- Video: LectureChain Rule: One Independent Variable
  . Duration: 7 minutes

Practice QuizPractice Quiz • 30 min30 minutes

Practice Quiz #2

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Practice Quiz #2

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Practice Quiz #2

Total points 3

1.

Question 1

Choose all correct statements:

2 / 2 points

The first differential is the linear (plane) part of the change of the function

Correct

Correct!

The number of second partial derivatives of the functions of $n$ variables is $n^2$ if all of them are smooth enough

Derivatives $f''_{xy}$ and $f''_{yx}$ formally differ but in most case coincide

Correct

Correct!

Convexity of the function of two variables is determined by all-positive second derivatives in the given point

2.

Question 2

Consider function $e^{ax+by}$ . Find the value $D=f''_{xx} \cdot f''_{yy}-(f''_{xy})^2$ .

1 / 1 point

0

0

Correct

How do you think, it makes our function convex or concave?